Prove that `|[a^2+2a,2a+1,1],[2a+1,a+2,1],[3,3,1]|=(a-1)^3`

Explanation

To prove that the determinant

\[
D = \begin{vmatrix}
a^2 + 2a & 2a + 1 & 1 \\
2a + 1 & a + 2 & 1 \\
3 & 3 & 1
\end{vmatrix}
...